Answer Key • Lesson 3: Using Ratios
Student Guide
1. What patterns do you see in Edward’s table?
2. How could you continue the table by using multiplication?
3. What patterns do you think Edward sees in both the table and graph?
Describe the patterns in your own words.
4. A. Use the graph to find the cost of seven muffins.
B. If a customer has $1.50, how many muffins can he or she buy?
5. A. Copy and complete the table for the cost of cookies.
Cost of Cookies
Number of
Cookies
2
$1.00
B. Make a graph of the data. Graph the number of cookies on the
horizontal axis and the cost on the vertical axis. Use Centimeter Graph
Paper.
6. A. What patterns do you see in the table in Question 5?
B. What patterns do you see in the graph?
C. Describe any patterns you see in both the table and graph.
7. A. Use your graph in Question 5B to find the cost of 1 dozen (12) cookies.
B. What is the cost of three cookies?
Using Ratios
Student Guide - Page 224
Cost
2
25¢
4
50¢
6
75¢
8
$1.00
6. A. Answers will vary. Some possible patterns
include: the numbers in the second column
are multiples of 25¢, doubling the number
of cookies doubles the cost, etc.
B. Answers will vary. Students should see
similar patterns in the graph as in the table.
As the number of cookies increases by two,
the cost increases by 25¢.
C. Answers will vary. The table and graph
show that as the number of cookies doubles,
so does the cost. As the number of cookies
increases by two, the cost increases by 25¢.
7. A.* $1.50; See graph in Q# 5B.
B.
Cost of Cookies
$1.50
Question 7A
$1.25
C
Cost in Cents
SG • Grade 5 • Unit 5 • Lesson 3
Cost of Cookies
Number of
Cookies
Copyright © Kendall Hunt Publishing Company
25¢
6
224
5. A.
Cost
Copyright © Kendall Hunt Publishing Company
Using Ratios (SG pp. 224–227)
Questions 1–17
1.* Answers will vary. Some possible patterns
include: the numbers in the second column are
multiples of 30¢, the cost of the muffins is 30¢
times the number of muffins, doubling the
number of muffins doubles the cost, etc.
2.* Answers will vary. Students can double the
number of muffins, which doubles the cost
or they can multiply the number of muffins
by 30¢.
3.* Answers will vary. The table and graph show
that as the number of muffins increases by one,
the cost of the muffins increases by 30¢.
4. A.* $2.10; See the graph in Figure 2 in the
Lesson.
B.* 5 muffins; See the graph in Figure 2 in the
Lesson.
B.* 37 21 cents; or more practically, 38¢
$1.00
75¢
50¢
Question 7B
Question 15B
25¢
0
0
2
4
6
8 10 12
N
Number of Cookies
14
*Answers and/or discussion are included in the lesson.
TG • Grade 5 • Unit 5 • Lesson 3 • Answer Key 1
Answer Key • Lesson 3: Using Ratios
8. Answers will vary. Two possible ratios include:
4 cookies for 50¢ and 6 cookies for 75¢.
Comparison of Yards to Feet
9.
Ratios
Edward and Frank used ratios to help them with the prices for the bake sale. A
ratio is a way to compare two numbers or quantities. When they were finding out
prices of muffins, they used the ratio “1 muffin costs 30 cents.” They found equal
ratios: “2 muffins cost 60 cents” and “3 muffins cost 90 cents.”
Number of Yards
8. Use your table or graph in Question 5 to name two ratios equal to the ratio
“2 cookies for 25¢.”
The decorating committee plans to decorate the gym with crepe paper, ribbon,
and balloons.
Number of Feet
2
6
5
15
6
18
7
8
21
10
30
24
Copyright © Kendall Hunt Publishing Company
10. 7 yards
11. Answers will vary. Two possible ratios include:
The committee measured the length and width of the gym in yards and the height
of the booths in feet. When they went to the store, they found that ribbon is sold
by the yard and the measurements on the packages of crepe paper are given in
feet. One way to convert feet to yards and yards to feet is by making and using a
graph. The students made a graph that compares feet to yards and yards to feet.
9 feet
3 yards
SG • Grade 5 • Unit 5 • Lesson 3
225
Student Guide - Page 225
14.
2 yards 4 yards
,
.
6 feet 12 feet
feet
feet
30 yards; 13 yard
3090yards
90 feet; 13 yard
3090yards
.
feet
feet
15. A.* No, 1 cookie for 15¢ means 2 cookies
for 30¢.
B.* No, the point falls on the line only if the
ratio is equal.
Ratios can be written as fractions. To compare feet and yards, we can write the
3 feet
⫺. We can write number sentences using fractions that show ratios are equal.
ratio ⫺
1⫺
yard
When the fractions are equal, the ratios are equal:
Comparison of Yards to Feet
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
3 feet
6 feet
⫽
1 yards
2 yards
3 feet
15 feet
and 1 yard ⫽ 5 yards
10. Complete the following number sentence:
3 feet
1 yard
⫽
21 feet
? yards
.
You can also compare feet to yards by looking at the ratio of yards to feet.
For example:
1 yard
2 yards
5 yards
⫽
⫽
3 feet
6 feet
15 feet
11. Using fractions, write two other ratios that are equal to
3 feet
1 yard
12. Using fractions, write two other ratios that are equal to
.
1 yard
3 feet
.
13. Ninety feet of crepe paper is needed to decorate one wall of the gym. How
many yards are needed to decorate that wall?
14. Frank decided to decorate each booth with 10 lengths of ribbon. Each
length of ribbon is 3 yards long. How many feet of ribbon are needed to
decorate each booth?
2
3
4
5
6
7
8
9
10
Y
Number of Yards
9. Copy the table below and use the graph to fill in the missing values.
Comparison of Yards to Feet
Number of Yards
Number of Feet
25¢
15¢
ᎏᎏ
ᎏᎏ
2 cookies and 1 cookie
Copyright © Kendall Hunt Publishing Company
1
Copyright © Kendall Hunt Publishing Company
0
15. Edward and Frank decided to sell 1 cookie for 15¢.
A. Are the following two ratios equal? Why or why not?
2
15
6
21
B. Add a point to the graph you made for Question 5 that shows that
1 cookie costs 15¢. Is this point on your line? Why or why not?
30¢
16. Using fractions, write two ratios that are equal to ⫺
⫺⫺.
1⫺
muffin
25¢
17. Using fractions, write two ratios equal to ⫺2⫺
⫺⫺⫺.
cookies
24
Use the Cost of Brownies pages in the Student Activity Book to practice using
ratios.
10
226
SG • Grade 5 • Unit 5 • Lesson 3
Using Ratios
Student Guide - Page 226
Using Ratios
Student Guide - Page 227
*Answers and/or discussion are included in the lesson.
2
TG • Grade 5 • Unit 5 • Lesson 3 • Answer Key
SG • Grade 5 • Unit 5 • Lesson 3
227
Copyright © Kendall Hunt Publishing Company
F
Number of Feet
18 feet
.
6 yards
12. Answers will vary. Two possible ratios include:
13.
Using Ratios
and
Answer Key • Lesson 3: Using Ratios
16. Answers will vary. Two possible ratios
include:
60¢
2 muffins
and
90¢
3 muffins
.
Graphs and Ratios
17. Answers will vary. Two possible ratios
include:
50¢
4 cookies
and
75¢
6 cookies
You will need enough graph paper to make three or four graphs.
1. A. The fifth graders decided to make data tables to help the first graders
use coins to pay for games and food at the fun fair. Copy and complete
the tables on your paper. Fill in at least 5 rows in each table.
.
Nickels to Dimes
Number of
Nickels
Number of
Dimes
2
1
Quarters to Dimes
Number of
Quarters
Number of
Dimes
2
5
4
Number of
Nickels
Number of
Dimes
2
1
4
2
6
3
8
4
10
5
B. Make a graph that compares the value
of dimes to the value of nickels. (Put
the number of nickels on the horizontal
axis and the number of dimes on the
vertical axis.) Draw a best-fit line.
C. Use fractions to write three ratios equal
dime
.
to 21nickles
D. Make a graph that compares the value
of dimes to the value of quarters. (Put
quarters on the horizontal axis.) Draw
a best-fit line.
E. Use fractions to write three ratios equal to
228
5 dimes
2 quarters
Copyright © Kendall Hunt Publishing Company
Homework (SG pp. 228–229)
Questions 1–4
Nickles to Dimes
1. A.
.
SG • Grade 5 • Unit 5 • Lesson 3
Using Ratios
Student Guide - Page 228
B.
Number of
Dimes
2
5
4
10
6
15
8
20
10
25
C. Answers will vary. Three possible ratios
dimes
include: 42nickles
,
D.
10
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
N
Number of Nickels
3 dimes
,
6 nickles
and
4 dimes
8 nickles
Ratio of Dimes to Quarters
D
Number of Dimes
Number of
Quarters
Ratio of Dimes to Nickels
D
Number of Dimes
Copyright © Kendall Hunt Publishing Company
Quarters to Dimes
60
55
50
45
40
35
25
20
15
10
5
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Q
Number of Quarters
E. Answers will vary. Three possible ratios
include:
10 dimes 15 dimes
, ,
4 quarters 6 quarters
20 dimes
and 8 quarters .
TG • Grade 5 • Unit 5 • Lesson 3 • Answer Key 3
Answer Key • Lesson 3: Using Ratios
2. A.
Quarts to Gallons
Solve Problems with Ratios
Use tools and strategies to solve each problem.
2. There are four quarts in a gallon.
A. Make a table with at least 5 rows that can be used to convert quarts
to gallons.
.
B. Write three ratios equal to 41 quarts
gallon
3. The poster for the bake sale says that one dozen rolls costs $2.40.
A. How much will three dozen rolls cost?
B. How much will six rolls cost? Explain how you found your answer.
Use the graph below to answer the following questions.
C
Cost
Copyright © Kendall Hunt Publishing Company
4. A. What is the cost for three people to see a movie?
B. What is the cost for six people to see a movie?
C. A customer paid the ticket seller $35.00. How many tickets did
he buy?
D. Choose a point on the graph and write a ratio that shows the cost to
the number of people.
E. Write two other ratios equal to the ratio you wrote in Question 4D.
$50.00
$45.00
$40.00
$35.00
$30.00
$25.00
$20.00
$15.00
$10.00
$5.00
0
Movie Prices
Gallons
4
1
8
2
12
3
16
4
20
5
B. Answers will vary. Three possible ratios
include:
8 quarts 12 quarts
, ,
2 gallons 3 gallons
16 quarts
and 4 gallons .
3. A. $7.20
B. $1.20; Explanations will vary. One possible
explanation is to take half of $2.40 since
6 rolls is half of one dozen.
0 1 2 3 4 5 6 7 8 9 10 11 12
N
Number of People
Using Ratios
SG • Grade 5 • Unit 5 • Lesson 3
229
Student Guide - Page 229
TG • Grade 5 • Unit 5 • Lesson 3 • Answer Key
$15.00
$30.00
7 tickets
Answers will vary. One possible ratio is
$5.00
.
1 person
E. Answers will vary. Two possible ratios
$10.00
$15.00
include: 2 people and 3 people .
4. A.
B.
C.
D.
Copyright © Kendall Hunt Publishing Company
4
Quarts
Answer Key • Lesson 3: Using Ratios
Student Activity Book
Name
Cost of Brownies (SAB pp. 207–209)
Questions 1–5
Date
Cost of Brownies
1. A.* See Figure 4 in the lesson.
B.* See Figure 5 in the lesson.
C.* Answers will vary. Possible response:
The poster for the bake sale says that brownies cost 50¢ each or $3.00 for eight.
$4
$1
$2
2 brownies = 4 brownies = 8 brownies
1. A. Complete the data table to show the cost if brownies are sold for
50¢ each.
D.* $6. Possible response: Show dotted lines
on the graph as shown on the graph in
Figure 5.
$9
$3
$6
8 brownies = 16 brownies = 24 brownies
D.* $18. Possible response: I saw a doubling
pattern in the table. The table shows that
24 brownies cost $9, so 48 brownies will
cost $18.
3.* The two lines are straight and start at (0, 0).
They go uphill. The one for 50¢ brownies is
steeper.
$4
$3
and 8 brownies
4. 8 brownies
. Possible response:
$4
$
The ratio of 8 brownies is larger
than the ratio
$3
of 8 brownies .
$1
8
16
B. Use the data table to make a graph that shows Cost vs. Number of
Brownies. Scale the horizontal axis by twos and the vertical axis by
ones. If the points form a line, draw a line through them.
N
C. Write three equal ratios that compare the Cost to the Number of
Brownies. Write the ratios as fractions.
D. How much will 12 brownies cost? Show or tell how you know.
Using Ratios
SAB • Grade 5 • Unit 5 • Lesson 3
207
Student Activity Book - Page 207
Name
Date
2. A. Complete the data table to show the cost if brownies are sold for $3.00
for a box of eight.
Cost of Brownies in a Box
5.* Possible response: If I want a few brownies, I
would spend 50¢ each, but if I want more than
six, I would buy them by the box. Six brownies
would cost $3.00 if bought individually, so I
might as well buy a box of 8 for $3.00.
Copyright © Kendall Hunt Publishing Company
Cost (in Dollars)
2
4
Copyright © Kendall Hunt Publishing Company
2. A.* See Figure 4 in the lesson.
B.* See Figure 5 in the lesson.
C.* Answers will vary. Possible response:
Cost of Brownies
Number of Brownies
Number of Brownies
Cost (in Dollars)
8
$3
16
24
B. Use the data table to make a graph that shows Cost vs. Number of
Brownies. Use the same graph paper that you used for Question 1B. If
the points form a line, draw a line through them.
C. Write three equal ratios that compare the Cost to the Number of
Brownies. Write the ratios as fractions.
D. How much will 48 brownies cost? Show or tell how you know.
3. Describe the two lines on your graph. How do they compare?
4. Write a ratio for the Cost to the Number of Brownies for each line when the
Number of Brownies is 8. How do the two ratios compare?
5. Would you rather buy brownies individually or in boxes of eight? Explain
your thinking.
208
SAB • Grade 5 • Unit 5 • Lesson 3
Copyright © Kendall Hunt Publishing Company
E. How do you know your answer to Question 2D is reasonable?
Using Ratios
Student Activity Book - Page 208
*Answers and/or discussion are included in the lesson.
TG • Grade 5 • Unit 5 • Lesson 3 • Answer Key 5